Showing papers in "International Journal of Control in 2011"

Control of nonlinear systems with partial state constraints using a barrier Lyapunov function

Abstract: This article addresses the problem of control design for strict-feedback systems with constraints on the states. To prevent the states from violating the constraints, we employ a barrier Lyapunov function (BLF), which grows to infinity whenever its arguments approaches some finite limits. Based on BLF-based backstepping, we show that asymptotic output tracking is achieved without violation of any constraint, provided that the initial states and control parameters are feasible. We also establish sufficient conditions to ensure feasibility, which can be checked offline without precise knowledge of the initial states. The feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem. In the presence of parametric uncertainties, BLF-based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation. To relax the feasibility conditions, asymme...

A survey on iterative learning control for nonlinear systems

Abstract: In this article we review the recent advances in iterative learning control (ILC) for nonlinear dynamic systems. In the research field of ILC, two categories of system nonlinearities are considered, namely, the global Lipschitz continuous (GLC) functions and local Lipschitz continuous (LLC) functions. ILC for GLC systems is widely studied and analysed using contraction mapping approach, and the focus of recent exploration moves to application problems, though a number of theoretical issues remain open. ILC for LLC systems is currently a hot area and the recent research focuses on ILC design and analysis by means of Lyapunov approach. The objectives of this article are to introduce recent development and advances in nonlinear ILC schemes, highlight their effectiveness and limitations, as well as discuss the directions for further exploration of nonlinear ILC.

On convergence of tracking differentiator

Abstract: The tracking differentiator was first proposed by Han in 1989 and the proof of convergence was presented the first time in Han and Wang (Han, J.Q., and Wang, W. (1994), ‘Nonlinear Tracking-differentiator’, Journal of Systems Science and Mathematical Science, 14, 177–183 (in Chinese)). Unfortunately, the proof there is incomplete. This problem has been open for over two decades. In this article, we give a rigorous proof under some additional conditions. An application for online estimation of the unknown frequencies for the finite sum of the sinusoidal signals is presented. The numerical simulations illustrate the effectiveness of the estimation for both linear and nonlinear tracking differentiators.

Terminal iterative learning control based station stop control of a train

Abstract: The terminal iterative learning control (TILC) method is introduced for the first time into the field of train station stop control and three TILC-based algorithms are proposed in this study. The TILC-based train station stop control approach utilises the terminal stop position error in previous braking process to update the current control profile. The initial braking position, or the braking force, or their combination is chosen as the control input, and corresponding learning law is developed. The terminal stop position error of each algorithm is guaranteed to converge to a small region related with the initial offset of braking position with rigorous analysis. The validity of the proposed algorithms is verified by illustrative numerical examples.

Adaptive discrete-time controller design with neural network for hypersonic flight vehicle via back-stepping

Abstract: In this article, the adaptive neural controller in discrete time is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle. The dynamics are decomposed into the altitude subsystem and the velocity subsystem. The altitude subsystem is transformed into the strict-feedback form from which the discrete-time model is derived by the first-order Taylor expansion. The virtual control is designed with nominal feedback and neural network (NN) approximation via back-stepping. Meanwhile, one adaptive NN controller is designed for the velocity subsystem. To avoid the circular construction problem in the practical control, the design of coefficients adopts the upper bound instead of the nominal value. Under the proposed controller, the semiglobal uniform ultimate boundedness stability is guaranteed. The square and step responses are presented in the simulation studies to show the effectiveness of the proposed control approach.

Vibration control of an Euler–Bernoulli beam under unknown spatiotemporally varying disturbance

Abstract: In this article, the vibration suppression of an Euler–Bernoulli beam system is considered by using the adaptive boundary control technique. The dynamics of the beam are represented by a partial differential equation and four ordinary differential equations involving functions of both space and time. By using Lyapunov synthesis, the robust boundary control with a disturbance observer is first proposed to suppress the vibration and attenuate the effect of the external disturbances. To compensate for both the system parametric uncertainties and the disturbances uncertainties, the adaptive boundary control is developed. With the proposed boundary control, the state of the beam system is proven to be uniformly ultimately bounded and converge to a small neighbourhood of zero by appropriately choosing the design parameters. The effectiveness of the proposed control is successfully verified by numerical simulations.

A virtual structure approach to formation control of unicycle mobile robots using mutual coupling

Abstract: In this article, the formation control problem for unicycle mobile robots is studied. A distributed virtual structure control strategy with mutual coupling between the robots is proposed. The rationale behind the introduction of the coupling terms is the fact that these introduce additional robustness of the formation with respect to perturbations as compared to typical leader–follower approaches. The applicability of the proposed approach is shown in simulations and experiments with a group of wirelessly controlled mobile robots.

A triangular canonical form for a class of 0-flat nonlinear systems

Abstract: This article proposes a triangular canonical form for a class of 0-flat nonlinear systems. Necessary and sufficient geometrical conditions are given in order to guarantee the existence of a local diffeomorphism to transform the studied nonlinear systems into the proposed 0-flat canonical form, which enables us to compute the flat output as well.

Positive observers for linear positive systems, and their implications

Abstract: A treatment of the positive observation problem for positive systems is provided, for the continuous and discrete-time cases. The proposed observers are positive, that is, they ensure that the estimates are nonnegative at any time. Moreover, necessary and sufficient conditions for the existence of such positive observers are formulated in terms of linear programming. Also, we show how positive observers can provide guaranteed bounds on the real states of uncertain positive systems. In addition, some implications are discussed; especially, it is shown that it is not possible to stabilise an unstable system using these positive observers. Finally, the applicability of the proposed interval estimation approach is shown for an illustrative application from pharmacokinetics.

Robust consensus tracking for an integrator-type multi-agent system with disturbances and unmodelled dynamics

Abstract: In this article, a robust consensus tracking problem for a multi-agent system with integrator-type dynamics has been addressed in the presence of disturbances and unmodelled dynamics. The desired trajectory to be tracked is only provided to a small group of team members. An identifier is developed to estimate the unknown disturbances and unmodelled dynamics. A consensus controller is developed based on this identifier to achieve asymptotic consensus tracking using the local information obtained from neighbouring agents. The closed-loop stability is proved using the Lyapunov-based analysis and an invariance-like theorem. Numerical simulations are provided to demonstrate the effectiveness of the developed robust consensus controller.

A Google-like model of road network dynamics and its application to regulation and control

Abstract: Inspired by the ability of Markov chains to model complex dynamics and handle large volumes of data in Google's PageRank algorithm, a similar approach is proposed here to model road network dynamics. The central component of the Markov chain is the transition matrix which can be completely constructed by easily collecting traffic data. The proposed model is validated using the popular mobility simulator SUMO. Markov chain theory and spectral analysis of the transition matrix are then shown to reveal non-evident properties of the underlying road network and to correctly predict consequences of road network modifications. Preliminary results from possible applications are shown and simple practical examples are provided throughout this article to clarify and support the theoretical expectations.

Online robust tube-based MPC for time-varying systems: a practical approach

Abstract: This article focuses on the design of a robust model predictive control law for constrained discrete-time time-varying systems with additive uncertainties. The proposed solution to the control problem is a tube-based MPC ensuring robustness and constraints fulfilment. Reachable sets are calculated online taking into account the system dynamics by means of an adaptive local control law and additive uncertainties. The proposed method represents a trade-off between small conservativeness and efficient real-time execution. This approach is applied to solve the trajectory tracking problem of a mobile robot. Simulation results provide a comparison between the tube-based MPC scheme and established motion control algorithms, showing the efficient execution and satisfactory behaviour of the proposed controller.

Design of structured dynamic output-feedback controllers for interconnected systems

Abstract: We address the design of structured controllers for networks of interconnected multivariable discrete-time subsystems. Different from existing approaches, where the structure of the controller is fixed a priori, we aim to design decentralised controllers such that each subsystem has a controller, which may not only use the output of its own associated subsystem, but also selected outputs of other subsystems. The total number of all those additional outputs used is to be minimised, while satisfying a guaranteed level of ℋ∞-performance. For the resulting non-convex optimisation problem, we first present a novel characterisation of the ℋ∞-performance of the closed-loop system by means of a system augmentation approach. Then, stimulated from compressive sensing theory, we propose a weighted l1-minimisation to relax the l0 objective function for structure optimisation. We develop an algorithm to deal with the relaxed decentralisation control problem, where the controller is obtained by iteratively solving conv...

A switching system approach to sensor and actuator assignment for stabilisation via limited multi-packet transmitting channels

Abstract: The problem of joint design of dynamic output feedback controller and network access assignment sequences of both input and output channels is investigated for networked control systems which have insufficient communication channels to simultaneously accommodate all the sensors and actuators. The sensors and the actuators are supposed to operate independently with individual communication packets and subject to successive time-varying delays and packet dropouts. A linear matrix inequality-based design method for dynamic output feedback controllers that are asymptotically stabilising and less conservative is derived using a model transformation technique and an improved Lyapunov–Krasovskii function. At the same time, a switching rule for assigning communication channels among the sensors and actuators while guaranteeing that the closed-loop system is asymptotically stable is suggested in the framework of switching system theory. Numerical examples are provided to show the usefulness and efficiency of the d...

Robust admissibility of uncertain switched singular systems

Abstract: This article investigates the robust admissibility of uncertain discrete-time switched singular systems. First, the admissibility is introduced, by using the switched Lyapunov function, for singular systems. Sufficient conditions for robust admissibility of uncertain switched singular systems are presented in strict linear matrix inequalities formulation. Robust admissibility condition designs for both state feedback and static output control feedback are then derived. Numerical examples are provided to illustrate our approach.

Linear quadratic output tracking and disturbance rejection

Abstract: This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.

Finite-time consensus for stochastic multi-agent systems

Abstract: In this article, we study the finite-time consensus in probability for stochastic multi-agent systems. First, we give the nonlinear consensus protocol for multi-agent systems with Gaussian white noise, and define the concept of finite-time consensus in probability. Second, we prove that multi-agent systems can achieve the finite-time consensus in probability under five different kinds of communication topologies by using graph theory, stochastic Lyapunov theory and probability theory. Finally, some simulation examples are provided to illustrate the effectiveness of the theoretical results.

L 2-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation

Abstract: The problem of L 2-gain analysis and control synthesis is studied for a class of uncertain discrete-time switched linear systems with time delay and saturating actuators by using the multiple Lyapunov functions method. With the state feedback controllers adopted beforehand, an analysis condition on disturbance tolerance is derived under which the operating state trajectory with zero initial condition will remain inside a bounded set in its proximity. Then with this condition at hand, the largest disturbance tolerance level is determined via the solution of a constrained optimisation problem. Then, a sufficient condition for the restricted L 2-gain over the set of tolerable disturbances is derived. The smallest upper bound on the restricted L 2-gain is also obtained by solving a constrained optimisation problem. Furthermore, when controller gain matrices are design variables, these optimisation problems are adjusted for solving the control design task. An illustrative numerical example is given to demonstr...

Global synchronised regions of linearly coupled Lur'e systems

Abstract: This article addresses the global synchronisation problem of a network of coupled Lur'e systems from the perspective of global synchronised region. A decomposition approach is proposed to convert the synchronisation of high-dimensional Lur'e networks into the test of a set of matrix inequalities whose dimensions are the same as a single Lur'e node. The notion of global synchronised region is then introduced and analysed. A necessary and sufficient condition is derived for the existence of the inner-linking matrix to guarantee a desirable unbounded synchronised region. A multi-step design procedure is given for constructing such an inner-linking matrix, which maintains a favourable decoupling property. Furthermore, the global H ∞ synchronised region is characterised for evaluating the performance of a Lur'e network subject to external disturbances. The effectiveness of the theoretical results is demonstrated through a network of Chua's circuits.

MPC for LPV systems with bounded parameter variations

Abstract: This article deals with the model predictive control (MPC) design problem for systems which are linearly dependent on a time-varying parameter. The main novelty is that, motivated by practical issues, the bounds on the rate of variation of the parameters are taken into account in the control design. Moreover, a Lyapunov function depending multiaffinely on the parameters computed at a set of instants of time and a parameter-dependent control gain are used to provide an upper bound to a quadratic performance index. The solution is obtained by means of a semidefinite programming algorithm. Examples illustrate the efficiency of the proposed approach.

Cross-coupled iterative learning control of systems with dissimilar dynamics: design and implementation

Abstract: Cross-coupled iterative learning control has previously been applied to contour tracking problems with planar manufacturing robots in which both axes can be characterised as similar systems; having similar dynamics and identical hardware. However, there are many repetitive applications in which dynamically dissimilar systems cooperate to pursue a primary performance objective. This article introduces a novel framework to couple dynamically dissimilar systems while applying iterative learning control, showing the ability to noncausally compensate for a slow system with a fast system. In this framework, performance requirements for a primary objective can more readily be achieved by emphasising an underutilised fast system instead of straining a less-capable slow system. The controller is applied to a micro-robotic deposition manufacturing system to coordinate a slow extrusion system axis and a fast positioning system axis to pursue the primary performance objective, dimensional accuracy of a fabricated par...

Finite-dimensional observer-based control of linear distributed parameter systems using cascaded output observers

Abstract: The synthesis of compensators for linear distributed-parameter systems on the basis of a finite-dimensional approximation is a classical technique. This so-called early-lumping approach suffers from the occurrence of spillover which means that the closed-loop dynamics is deteriorated by the neglected dynamics. In this contribution, an early-lumping compensator design is presented that overcomes the spillover problem by using certain fictitious outputs which can be reconstructed without spillover and that suppress the contributions of the unmodelled dynamics. When the new outputs are used for the compensator instead of the available measurements, the perturbation of the closed-loop spectrum, caused by spillover, can be reduced to an arbitrary extent. It is shown that the worst-case eigenvalue perturbation decreases exponentially with respect to the compensator order so that the spillover can be reduced systematically. In addition, an a priori estimate for the compensator order, that guarantees a prescribed...

Design and experimental validation of UDE based controller--observer structure for robust input--output linearisation

Abstract: In this work, uncertainty and disturbance estimation (UDE) technique is employed to robustify an input--output linearisation (IOL) controller. An IOL controller designed for a nominal system is augmented by the UDE estimated uncertainties to achieve robustness. In doing so, state dependent nonlinearities of the system are treated as a part of the uncertainties and thus, the controller does not require system states for its implementation. The resulting controller, however, needs derivatives of the output. To address the issue, a design of an observer that employs the UDE estimated uncertainties for robustness is proposed giving rise to the UDE based controller--observer structure. Closed loop stability of the overall system is established. The notable feature of the proposed design is that it neither requires accurate plant model nor system states or derivatives of output. Also the approach does not need any information about the uncertainty. To demonstrate the effectiveness, numerical simulation results ...

A curve extension design for coordinated path following control of unicycles along given convex loops

Abstract: This article utilises a dynamic model of unicycles to address the convergence of vehicle formation about closed convex curves. A novel curve extension method, extending the target loop along the vector from the loop centre to the point on the loop, is proposed to construct a family of level curves and the existence of a loop function on a tubular-like neighbourhood is proved by referring to the tubular neighbourhood theorem. Path following control is derived based on the loop function which incorporated into the arc-length function to propose the solution to coordinated formation control. We show how backstepping technique, Lyapunov-based theory and graph theory can be combined together to construct the coordinated path following controller under the bidirectional commutation topology. It is proved that the designed cooperative control system is asymptotically stable if the graph is connected. The proposed method is effective for a skewed superellipse, which is a type of curve that includes circles, ellip...

On the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form

Abstract: This article deals with the transformation of a class of nonlinear systems into an extended nonlinear observable canonical form (ENOCF) by dynamic extension. The dynamic extension is obtained by adding auxiliary dynamics and virtual outputs to the original system, thus giving rise to a higher dimensional system in an extended state space. Sufficient geometrical conditions to guarantee the existence of a local diffeomorphism which allow the transformation of the extended system into the ENOCF are given. In particular, an algorithm that permits us to compute such a diffeomorphism is derived.

Iterative learning control and repetitive control

Abstract: This special issue contains selected contributions originating from the ‘Symposium on Learning Control’ which took place immediately prior to the 2009 IEEE Conference on Decision and Control in Shanghai. This two day event was held at Shanghai Jiaotong University to commemorate 25 years of highly creative and productive research since the concept of Iterative Learning Control (ILC) was formally proposed by Professor Arimoto in the seminar paper (Arimoto, Kawamura, and Miyazaki 1984). The symposium was organised by up-and-coming members of the ILC research community, aided by an advisory committee of leading figures in the field. As well as being guest of honour at the event, Professor Arimoto delivered one of the plenary lectures. In Arimoto, Kawamura and Miyazaki (1984) a controller was presented that was applicable to systems which were required to track a desired reference trajectory that was of a fixed length T, and specified a priori. After each trial of the task, resetting of the system states occurred, during which time the measured output was used to construct the next control output. The system dynamics were assumed trial-invariant and invertible. In postulating the six tenets of ILC that are highlighted in bold, Professor Arimoto succeeded in creating a fertile framework which went on to rapidly attract research interest from multiple quarters around the world. ‘Bettering Operation of Robots by Learning’ has since been cited over 1258 times by researchers in over 45 counties. Prior to the formalisation of ILC, similar ideas of learning can be traced back to a patent filed in 1967 which proposed correcting command signals using characteristics of actuators which were learnt over time (United States Patent 3,555,252 1971). Closely related papers appeared on the control of multipass processes in Edwards (1974) and in a Japanese language paper which used a similar algorithm to control a mechanical arm in Uchiyama (1978). As well as providing a framework to support the rich stream of research which followed, Professor Arimoto has made substantial contributions to learning control applied to robotics, learning under geometric constraints, higher level learning, passivity and impedance, and control of multiple manipulators and hands. In the course of over a quarter-century, ILC has broadened in breadth and depth, fusing with established fields such as robust, adaptive, and optimal control, as well as neural networks, fuzzy logic and many others. Application areas have also expanded, most heavily in robotics, rotary systems, process control, bio-applications, power systems and semiconductors. Whilst ILC is still a relatively young field, with a combined body of research work amassing around 1/30th of more established areas, there is a strong linear trend in increasing year on year publications continually pushing the realms of both theory and applications. For recent state of the art, the review paper (Ahn, Chen, and Moore 2007) contains 515 references, with a further review paper containing 135 (Bristow, Tharayil, and Alleyne 2006). Numerous events have punctuated the rise in ILC research activity, including special sessions at the American Control Conference and IFAC World Congress over multiple years, tutorials and workshops at the Conference on Decision and Control, International Conference on Control, Automation, Robotics and Vision, and International Conference on Mechatronics and Automation. Several of Arimoto’s original six postulates have been relaxed in recent years, whilst the concept of learning from experience gained over repetitions of a task remains unchanged. This is especially true for linear ILC applied to linear plants, in the domain of which algorithms have emerged with variable trial length, imprecise resetting, a reference and output which are only defined over a subset of data points, and application of constraints of various forms. The mature algorithmic development in this area has given rise to a concerted effort on pushing the bounds of achievable performance, together with new analytical methods often inspired by practical demands. For nonlinear systems, the primarily focus of linear ILC has shifted towards practical control problems and associated theoretical challenges, whilst interest in nonlinear methodologies has gathered pace. Similar observations apply for Repetitive Control (RC), a closely related methodology in which no resetting occurs between trials. The seven papers in this special issue cover a broad spectrum of the current research landscape for ILC and RC. The collection starts with two papers on RC which are associated with a broadening in scope and performance. An RC approach for uncertain systems is

Sliding mode control-based algorithms for consensus in connected swarms

Abstract: In this article, finite-time consensus algorithms for a swarm of self-propelling agents based on sliding mode control and graph algebraic theories are presented. Algorithms are developed for swarms that can be described by balanced graphs and that are comprised of agents with dynamics of the same order. Agents with first and higher order dynamics are considered. For consensus, the agents' inputs are chosen to enforce sliding mode on surfaces dependent on the graph Laplacian matrix. The algorithms allow for the tuning of the time taken by the swarm to reach a consensus as well as the consensus value. As an example, the case when a swarm of first-order agents is in cyclic pursuit is considered.

H∞ predictive control of networked control systems

Abstract: This article is concerned with the problem of H ∞ predictive control of networked control system with random network delay. A new control scheme termed networked predictive control is proposed. This scheme mainly consists of the control prediction generator and network delay compensator. While designing the predictor, the control input to the actuator may be different due to networked induced time-delay and data dropout, and two cases are considered depending on the way that the observer obtains the plant control input u t . The necessary and sufficient conditions are given for the closed-loop networked predictive control system to be stochastically stable for different u t and random network delays in controller to actuator channel (CAC) and sensor to controller channel (SCC). A simulation study shows the effectiveness of the proposed scheme.

Generalised finite-frequency KYP lemma in delta domain and applications to fault detection

Abstract: This article generalises the Kalman--Yakubovi[cbreve]--Popov (KYP) lemma in delta domain to treat some conditions on different restricted frequency ranges. The frequency ranges are characterised by two quadratic forms. This characterisation encompasses low/middle/high frequency conditions for delta operator systems. By utilising the obtained delta domain generalised KYP lemma, a fault detection filter design problem is dealt with for delta operator systems in finite-frequency domain. The fault detection filter design problem is formulated as a two-objective optimisation algorithm with H − and H ∞ performance indexes. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.

Operator-based robust control design for nonlinear plants with perturbation

Abstract: In this article, operator-based robust control design for nonlinear plants with perturbation is considered by using robust right coprime factorisation approach. In detail, the property of unimodular operator is studied, and a control design structure is proposed. Based on the proposed design scheme, the designed system is robustly stable. Also, output tracking performance can be realised simultaneously. Finally, the effectiveness of the proposed design scheme is demonstrated by a simulation example.